Question

Check whether the sets $A$ and $B$ are disjoint:
$A=\{3,6,9,12,.15,...\},B=\{19,24,29,34,39,...\}$

Answer 1

If two sets are disjoint then they have no common elements (or) Intersection of those sets is null set.

$A=\{3,6,9,12,\mathrm{15..........}\}$

$B=\{19,24,29,34,\mathrm{39.......}\}$

$\Rightarrow$ $A\cap B=\{24,\mathrm{39.......}\}$ [Since, $A\cap B=$ Common elements of set $A$ and set $B$.]

$\Rightarrow$ $A\cap B$ is not empty set.

So, $A$ and $B$ are not disjoint (because $A\cap B\ne \varphi )$